Forward Error Control (FEC) coding is used by communications systems to ensure reliable transmission of data across noisy communication channels. Based on Shannon's theory, these communication channels exhibit a fixed capacity that can be expressed in terms of bits per symbol at a given Signal to Noise Ratio (SNR), which is defined as the Shannon limit. One of the research areas in communication and coding theory involves devising coding schemes offering performance approaching the Shannon limit while maintaining a reasonable complexity. It has been shown that LDPC codes using Belief Propagation (BP) decoding provide performance close to the Shannon limit with tractable encoding and decoding complexity.
In a recent paper Yan Li and William Ryan, “Bit-Reliability Mapping in LDPC-Codes Modulation systems”, IEEE Communications Letters, vol. 9, no. 1, January 2005, the authors studied the performance of LDPC-coded modulation systems with 8PSK. With the authors' proposed bit reliability mapping strategy, about 0.15 dB performance improvement over the non-interleaving scheme is achieved. Also the authors show that gray mapping is more suitable for high order modulation than other mapping scheme such as natural mapping.